141 (b) Show that if X1, X2, ..., Xn in (a) have normal distribution, then Y also has a normal distribution with mean My and variance of. 6. Show that the geometric Brownian motion X, = euttoBy14. Show that iI two random variables Aj, 42 and fiddpolldoit, tidy are also uncorrelated 5 /15. Let X1, X2, . .., Xn be independent random variables with means /1, /2, . .., An and vari ances of , 02, . .., On, respectively. (a) Show that Y = a1 X1 + a2X2 + . . . + anXn has mean MY = all1 + azu2 + . . . + anun and variance of = ajo, + ago? + ... + ano